I learned how to sew on my mom's vintage 800 series Bernina. I have a Bernina now (Activa 230) because of it. Those old ones don't die.
My mother was in the local shop having hers serviced and someone offered her an insane price for it. She said no since she's not interested in a new machine.
So...if you can find an old mechanical machine, go for it. You don't need a $1000+ machine, but as others have said, learning to sew on a decent machine makes a huge difference. I second sewing classes- you'll learn something and meet other local sewers. Or if you're in a situation like me where there are no classes available, there are some good books out there and plenty of blogs. Don't give into the temptation to start with spandex though.
New machines are probably easier to find and evaluate though, and you have reminded me that at one point I was researching sewing machines for my kids. I found this blog post that might be helpful for you. It evaluates inexpensive, but good quality children's and entry level machines:
http://stashforgood.com/?p=1378I also like icemom's blog- lotta good stuff there.